Bibliographic record
Abstract
This thesis is about constructions of canonical metrics in complex non-Kähler geome-<br/>try, focusing in particular on balanced metrics satisfying special hermitian curvature conditions.<br/>More specifically, we adapt gluing strategies from Kähler geometry to obtain families<br/>of balanced metrics with special curvature properties, with particular relevance for the constructions of solutions of the Hull-Strominger system and the geometrization of balanced classes. More specifically, we show that: crepant resolutions of orbifolds with isolated singularities admitting singular Chern-Ricci flat balanced metrics can also be endowed with Chern-Ricci flat balanced metrics; small resolutions of smoothable Calabi-Yau singular threefolds with a finite family of Ordinary Double Points admit an approximately Chern-Ricci flat balanced metric; the blowup at a finite family of points of a compact Chern-Ricci flat balanced manifold always admits Chern-scalar constant balanced metrics. In all three cases we have a control on the Bott-Chern cohomology class of metrics constructed.<br/>Furthermore, we use representation theory techniques to construct special balanced<br/>metrics on the class of real simple Lie groups of inner type, as well as on the corresponding compact homogeneous spaces, on which we obtain that the metrics constructed are Chern-scalar with non-vanishing Chern-Ricci tensor, providing a family of compact complex manifolds with vanishing first Chern class and non-vanishing first Bott-Chern class. Moreover, we show that for this class of homogeneous spaces the Fino-Vezzoni conjecture holds.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".